Factroize `(i) x^2-1-2a-a^2` `(ii) 1+2ab-(a^2+b^2)`

1.	Factroize `(i) x^2-1-2a-a^2` `(ii) 1+2ab-(a^2+b^2)`
Answer» We have `(i) x^2-1-2a-a^2` ` =x^2-(1+2a+a^2)` `=x^2-(1+a)^2` `{x-(1+a)}{x+(1+a)}` `=(x-1-a)(x+1+a)`. `therefore (x^2-1-2a-a^2)=(x-1-a)(x+1+a)`. `(ii) 1+2ab-(a^2+b^2)` ` =1-(a^2+b^2-2ab)` ` =1^2-(a-b)^2` `={1-(a-b)}{(1+(a-b)}` `(1-a+b)(1+a-b)`. `therefore 1+2ab-(a^2+b^2)=(1-a+b)(1+a-b)`.

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